19877 ÷ 7 = 2839 R4
Alright, let's work through the division of 19877 by 7 step by step.

Step 1:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 7

Step 2:
7 goes into 19 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 14 from 19 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 7

Step 3:
7 goes into 58 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 28
Subtract 56 from 58 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 7

Step 4:
7 goes into 27 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 283
Subtract 21 from 27 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 7

Step 5:
7 goes into 67 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 2839
Subtract 63 from 67 to get 4.

The final result is 2839 with a remainder of 4.